Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $\chi({\bf q},\omega)$. The imaginary part, $\chi''({\bf q},\omega)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $\chi$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure $\chi({\bf q},\omega)$ at the meV energy scale relevant to modern elecronic materials. Here, we demonstrate a way to measure $\chi$ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as "M-EELS," allows direct measurement of $\chi''({\bf q},\omega)$ with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.Comment: 26 pages, 10 sections, 7 figures, and an appendi

Anharmonic multiphonon origin of the valence plasmon in SrTi1-xNbxO3

Doped SrTi1-xNbxO3 exhibits superconductivity and a mid-infrared optical response reminiscent of copper-oxide superconductors. Strangely, its plasma frequency, omega_p, increases by a factor of ~3 when cooling from 300 K to 20 K, without any accepted explanation. Here, we present momentum-resolved electron energy loss spectroscopy (M-EELS) measurements of SrTi1-xNbxO3 at nonzero momentum, q. We find that the infrared feature previously identified as a plasmon is present at large q in insulating SrTiO3, where it exhibits the same temperature dependence and may be identified as an anharmonic, multiphonon background. Doping with Nb increases its peak energy and total spectral weight, drawing this background to lower q where it becomes visible in IR optics experiments. We conclude that the "plasmon" in doped SrTi1-xNbxO3 is not a free-carrier mode, but a composite excitation that inherits its unusual properties from the lattice anharmonicity of the insulator.Comment: 5 pages, 4 figure

Non-RPA behavior of the valence plasmon in SrTi1−⁢ Nb⁢O3

Funding: We thank Dirk van der Marel, Alexey Kuzmenko, and Simone Fratini for helpful discussions. This work was supported by the Center for Quantum Sensing and Quantum Materials, a DOE Energy Frontier Research Center, under Award DE-SC0021238. P.A. acknowledges support from the EPiQS program of the Gordon and Betty Moore Foundation, Grant No. GBMF9452. M.M. acknowledges support from the Alexander von Humboldt Foundation. S.B. acknowledges support through the Early Postdoc Mobility Fellowship from the Swiss National Science Foundation, Grant No. P2EZP2 191885.Doped SrTi1-x NbxO3 is a dilute polaronic metal that exhibits superconductivity and a mid-infrared optical response suggesting parallels with copper oxides. A peculiar feature of SrTi1-x NbxO3 is that its plasma frequency, ωp, is highly temperature dependent, increasing by more than a factor of 2 when the system is cooled from 300 to 100 K [F. Gervais et al., Phys. Rev. B 47, 8187 (1993); D. M. Eagles et al., Phys. Rev. B 54, 22 (1996); C. Z. Bi et al., J. Phys.: Condens. Matter 18, 2553 (2006). There is still no generally accepted explanation for this dramatic shift. Here, we present momentum-resolved electron energy-loss spectroscopy measurements of SrTi1-x NbxO3 at nonzero momentum, q. We also calculate the collective excitations of SrTi1-x NbxO3 using the random phase approximation (RPA), to assess whether the behavior of the collective modes conforms to established explanations. We find that the plasmon energy and linewidth are momentum independent, in contrast to RPA predictions, and that its shift with temperature takes place everywhere in the Brillouin zone, from q=0 to the zone boundary, q=0.5 reciprocal lattice units. We also find that the phonon frequencies do not shift with q in the expected way, suggesting the screening properties of the material deviate significantly from RPA predictions. We conclude that a radically different starting point, perhaps based on lattice anharmonicity, may be needed to explain the collective charge excitations of SrTi1-x NbxO3.Peer reviewe

Pines’ demon observed as a 3D acoustic plasmon in Sr₂RuO₄

Sr2RuO4での「パインズの悪魔」の観測 67年前に予言された金属の奇妙な振る舞いの発見. 京都大学プレスリリース. 2023-08-10.Speak of the Demon: Discovery of strange behavior of new plasmons predicted in the 50s. 京都大学プレスリリース. 2023-09-25.The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a ‘demon’, could exist in three-dimensional (3D) metals containing more than one species of charge carrier. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected in an equilibrium, 3D metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals, optical properties of metal nanoparticles, soundarons in Weyl semimetals and high-temperature superconductivity in, for example, metal hydrides. Here, we present evidence for a demon in Sr₂RuO₄ from momentum-resolved electron energy-loss spectroscopy. Formed of electrons in the β and γ bands, the demon is gapless with critical momentum qc = 0.08 reciprocal lattice units and room-temperature velocity v = (1.065 ± 0.12) × 10⁵ m s⁻¹ that undergoes a 31% renormalization upon cooling to 30 K because of coupling to the particle–hole continuum. The momentum dependence of the intensity of the demon confirms its neutral character. Our study confirms a 67-year old prediction and indicates that demons may be a pervasive feature of multiband metals

Quasiparticle interference and strong electron-mode coupling in the quasi-one-dimensional bands of Sr2RuO4

The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound

Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $\chi({\bf q},\omega)$. The imaginary part, $\chi''({\bf q},\omega)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $\chi$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure $\chi({\bf q},\omega)$ at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure $\chi$ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as ``M-EELS" allows direct measurement of $\chi''({\bf q},\omega)$ with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-{\bf q} excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control

Signatures of exciton condensation in a transition metal dichalcogenide.

Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), we studied electronic collective modes in the transition metal dichalcogenide semimetal 1T-TiSe2 Near the phase-transition temperature (190 kelvin), the energy of the electronic mode fell to zero at nonzero momentum, indicating dynamical slowing of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials